NCERT Solutions for Class 6 Maths Chapter 7 Fractions

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Written by Team Trustudies
Updated at 2021-02-11


NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.6

Q.1 Solve
(a)23+17
(b)310+715
(c) 49+27
(d) 57+13
(e) 25+16
(f) 45+23
(g) 34?13
(h) 56?13
(i) 23+34+12
(j) 12+13+16
(k) 113+323
(l) 423+314
(m) 165?75
(n) 43?12



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a)23+17
LCM of 7 and 3 = 21
2×73×7+1×37×3
= 1421+321
= 1721
(b)310+715
LCM of 10 and 15 = 30
3×310×3+7×215×2
= 930+1430
= 2330
(c) 49+27
LCM of 9 and 7 = 63
4×79×7+2×97×9
= 2863+1863
= 4663
(d) 57+13
LCM of 7 and 3 = 21
5×37×3+1×73×7
= 1521+721
= 2221
(e) 25+16
LCM of 5 and 6 = 30
2×65×6+1×56×5
= 1230+530
= 1730
(f) 45+23
LCM of 5 and 3 = 15
4×35×3+2×53×5
= 1215+1015
= 2215
(g) 34?13
LCM of 4 and 3 = 12
3×34×3?1×43×4
= 912?412
= 512
(h) 56?13
LCM of 6 and 3 = 6
56?1×23×2
= 56?26
= 36 = 12
(i) 23+34+12
LCM of 3, 4 and 2 = 12
2×43×4+3×34×3+1×62×6
812+912+612
2312
(j) 12+13+16
LCM of 2, 3 and 6 = 6
1×32×3+1×23×2+16
36+26+16
66 = 1
(k) 113+323
= 43+113
= 153 = 5
(l) 423+314
= 143+134
LCM of 3 and 4 = 12
14×43×4+13×34×3
= 5612+3912
= 9512 \)
(m) 165?75
95 = 145
(n) 43?12
LCM of 3 and 2 = 6
4×23×2?1×32×3
= 86?36
= 56 \)

Q.2 Sarita bought 25 metre of ribbon and Lalita 34 metre of ribbon. What is the total length of the ribbon they bought?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Length of ribbon bought by Sarita = 25 metre
Length of ribbon bought by Lalita = 34 metre
? Length of ribbon bought by Sarita and Lalita 25+34
LCM of 5 and 4 = 20
2×45×4+3×54×5
= 820+1520
= 2320 = 1320 meter

Q.3 Naina was given 112 piece of cake and Najma was given 113 piece of cake. Find the total amount of cake was given to both of them.



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Fraction of cake Naina got = 112 = 32
Fraction of cake Najma got = 113= 43
Total amount of cake given to both of them =
32+43
LCM of 2 and 3 = 6
3×32×3+4×23×2
= 96+86
= 176 = 256

Q. 4. Fill in the boxes:
(a) ??58=14
(b) ??15=12
(c) 12??=16



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) ??58=14
Or, ?=14+58
= 1×24×2+58
= 28+58 = 78(b)\(??15=12
Or, ?=12+15
= 1×52×5+1×25×2
= 510+210 = 710
(C) 12??=16
Or, 12?16=?
Or, ?=1×32×3?16
Or, ?=36?16
Or, ?=26 = 13

Q.5 Complete the addition-subtraction box.



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Q6 A piece of wire 78 metre long broke into two pieces. One piece was 14 metre long. How long is the other piece?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Total length of wire = 78 metre
Length of one piece of wire = 14metre
Length of other piece of wire = Length of the original wire and this one piece of wire
= 78?14
= 78?1×24×2
= 78?28
= 58

Q.7 Nandini’s house is 910 km from her school. She walked some distance and then took a bus for 12 km to reach the school. How far did she walk?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Distance of the school from house = 910 km
Distance she travelled by bus = 12 km
Distance walked by Nandini = Total distance of the school – Distance she travelled by bus
= 910?12
= 910?1×52×5
= 910?510
= 410 = 25 km

Q.8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 56 th full and Samuel’s shelf is 25 th full. Whose bookshelf is more full? By what fraction?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Fraction of Asha’s bookshelf = 56
Fraction of Samuel’s bookshelf = 25
56 and 25
By cross multiplication
5×5 and 6×2
25 > 12
56 > 25
? Asha’s bookshelf is more full than Samuel’s bookshelf
Difference = 56 - 25
= 5×56×5 - 2×65×6
= 2530 - 1230
= 1330

Q.9 Jaidev takes215 minutes to walk across the school ground. Rahul takes74 minutes to do the same. Who takes less time and by what fraction?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Time taken by Jaidev to walk across the school ground =215 = 115 minutes
Time taken by Rahul to walk across the school ground = 74 minutes
115 and 74
By cross multiplication
11×4 and 5×7
44 > 35
115 > 74
? Rahul takes less time than Jaidev to walk across the school ground
Difference = 115 - 74
= 11×45×4 - 7×54×5
= 4420 - 3520
= 920

NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.1

Q.1 Write the fraction representing the shaded portion.



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(i) Number of parts = 4
Shaded portion = 2
? Fraction = 24
(ii) Number of parts = 9
Shaded portion = 8
? Fraction = 89
(iii) Number of parts = 8
Shaded portion = 4
? Fraction = 48
(iv) Number of parts = 4
Shaded portion = 1
? Fraction = 14
(v) Number of parts = 7
Shaded portion = 3
? Fraction = 37
(vi) Number of parts = 12
Shaded portion = 3
? Fraction = 312
(vii) Number of parts = 10
Shaded portion = 10
? Fraction = 1010
(viii) Number of parts = 9
Shaded portion = 4
? Fraction = 49
(ix) Number of parts = 8
Shaded portion = 4
? Fraction = 48
(x) Number of parts = 2
Shaded portion = 1
? Fraction = 12

Q.2 Colour the part according to the given fraction.



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Q.3 Identify the error, if any.



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(i) The parts are not equal
Hence, this is not 12
(ii) the parts are not equal
Hence, Shaded portion is not 14
(iii) the parts are not equal
Hence, Shaded portion is not 34

Q.4 What fraction of a day is 8 hours?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Since, a day has 24 hours and we have 8 hours
? Required fraction = 824

Q.5 What fraction of an hour is 40 minutes?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Since 1 hours = 60 minutes
? Fraction of 40 minutes = 4060

Q.6 Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) Arya has divided the sandwich into 3 equal parts. So each person will get one part.
(b) Each boy receive 13

Q.7 Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Total number of dresses to be dyed = 30
Number of dresses finished = 20
? Required fraction = 2030=23

Q.8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Natural numbers between 2 and 12 are;
2,3,4, 5, 6, 7, 8, 9, 10,11, 12
No. of given natural numbers = 11
No. of prime numbers = 5
Hence, fraction = 511

Q.9 Write the natural numbers from 102 to 113. What fraction of them are prime numbers?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Natural numbers from 102 to 113 are;
102,103,104,105,106, 107,108, 109,110, 111, 112,113
Total number of given natural numbers = 12
Prime numbers are 103, 107, 109, 113 Number of prime numbers = 4
Hence, fraction = 412 = 13

Q.10 What fraction of these circles have X’s in them?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Total number’of circles = 8
Number of circles having X’s in them = 4
Required fraction = 48=12

Q.11 Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Number of CDs bought by her from the market = 3
Number of CDs received as gifts = 5
Therefore Total number of CDs = 3 + 5 = 8
Therefore Fraction of CDs (bought) = 38
and the fraction of CDs (gifted) = 58

NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.2

Q.1 Draw number lines and locate the points on them:
(a)12,14,34,44
(b) 18,28,38,78
(c) 25,35,85,45



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :



Q.2 Express the following as mixed fractions:
(a)203
(b) 115
(c) 177
(d) 285
(e) 196
(f) 359



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a)203 = 623
(b) 115 = 215
(c) 177 = 237
(d) 285 = 535
(e) 196 = 316
(f) 359 = 389

Q.3 Express the following as improper fractions:
(a) 734
(b) 567
(c) 256
(d) 1035
(e) 937
(f) 849



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) (7×4+3)4=314

? The improper form is 314
(b) (5×7+6)7=417

? The improper form is 417
(c) (2×6+5)6=176

? The improper form is 176
(d) (10×5+3)5=535

? The improper form is 535
(e) (9×7+3)7=667

? The improper form is 667
(f) (8×9+4)9=769

? The improper form is 769

NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.3

Q.1 Write the fractions. Are all these fractions equivalent?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a)
(i) The shaded portion is 12
(ii) The shaded portion is24=12
(iii) The shaded portion is 36=12
(iv) The shaded portion is 48=12
Hence, all fractions are equivalent.
(b)
(i) The shaded portion is 412=13
(ii) The shaded portion is39=13
(iii) The shaded portion is 26=13
(iv) The shaded portion is 615=25
Hence, all fractions are not equivalent.

Q.2 Write the fractions and pair up the equivalent fractions from each row.



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a)12
(b) 46 = 23
(c) 39 = 13
(d) 28 = 14
(e) 34
(i) 618 = 13
(ii) 48 = 12
(iii) 1216 = 34
(iv) 812 = 23
(v) 416 = 14
The following are the equivalent fractions
(a) and (ii)
(b) and (iv)
(c) and (i)
(d) and (v)
(e) and (iii)

Q.3 Replace ?in each of the following by the correct number:
(a) 27=8?
(b) 58=10?
(c) 35=?20
(d) 4560=15?
(e) 1824=?4



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) 27=8?
? 2×47×4=828
(b) 58=10?
? 5×28×2=1016
(c) 35=?20
? 3×45×4=1220
(d) 4560=15?
? 45÷360÷3=1520
(e) 1824=?4
? 18÷624÷6=34

Q.4 Find the equivalent fraction of 35having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) We require denominator 20
Let M be the numerator of the fractions
?M20=\(35
5 × M = 20 × 3
M = (20 × 3) ÷ 5 = 12
Therefore the required fraction is 1220
(b) We require numerator 9
Let N be the denominator of the fractions
?9N=\(35
3 × N = 9 × 5
N = (9 × 5) ÷ 3 = 15
Therefore the required fraction is 915
(c) We require denominator 30
Let D be the numerator of the fraction
?D30=\(35
5 × D = 3 × 30
D = (3 × 30) ÷ 5
= 18
Therefore the required fraction is 1830
(d) We require numerator 27
Let X be the denominator of the fraction
?27X=\(35
3 × X = 5 × 27
X = (5 × 27) ÷ 3 = 45
Therefore the required fraction is 2745

Q.5 Find the equivalent fraction of 36 / 48 with
(a) numerator 9
(b) denominator 4



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) Given numerator = 9
?9X=3648

X × 36 = 9 × 48
X = (9 × 48) / 36
X = 12
Hence, the equivalent fraction is 912
(b) Given, denominator = 4
?X4=3648

X × 48 = 4 × 36
X = (4 × 36) / 48 = 3
Hence, the equivalent fraction is 34

Q.6 Check whether the given fractions are equivalent:
(a) 59,3054
(b) 310,1250
(c) 713,511



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) Given 59 and 3054
We have 5× 54 = 270
9 × 30 = 270
5 × 54 = 9 × 30
Hence, 59 and 3054 are equivalent fractions
(b) Given 310 and 1250
We have 3 × 50 = 150
10 × 12 = 120
3 × 50 ?10 × 12
Hence, 310 and 1250 are not equivalent fractions
(c) Given 713 and 511

We have 7 × 11 = 77
5 × 13 = 65
7 × 11 ? 5 × 13
Hence, 713 and 511 are not equivalent fractions

Q.7 Reduce the following fractions to simplest form:
(a) 4860
(b) 15060
(c) 8498
(d) 1252
(e) 728



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

(a) 4860 = 48÷1260÷12
= 45
(b) 15060 = 150÷3060÷30
= 52
(c) 8498= 84÷1498÷14
= 67
(d) 1252 = 12÷452÷4
= 313
(e) 728 = 7÷728÷7
= 14

Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?



NCERT Solutions for Class 6 Maths Chapter 7 Fractions


Answer :

Total number of pencils Ramesh had = 20
Number of pencils used by Ramesh = 10